Sir Jack Brabham, the only man to have won the Formula One drivers’ title in a car bearing his name, has died aged 88.

The Australian won world championships in 1959, 1960 and 1966, the last one in a Brabham. During a F1 career that stretched from 1955 to 1970 Brabham competed in 126 grands prix, winning 14. From 1955 to 1961 Brabham drove for the Cooper team before setting up as a constructor in his own right.

“It’s a very sad day for all of us,” his youngest son, David, said on the family’s website. “My father passed away peacefully at home at the age of 88 this morning. He lived an incredible life, achieving more than anyone would ever dream of and he will continue to live on through the astounding legacy he leaves behind.”

The grandson of a Londoner who emigrated to Australia, he was born in Hurstville, south of Sydney, the son of a greengrocer. Brabham joined the Royal Australian Air Force late in the second world war when he became a mechanic. After being demobbed in 1947 he started making a name for himself in motor sport and moved to Britain in the mid-1950s.

He made his debut in the 1955 British Grand Prix at Aintree in a rear-engined Cooper which soon proved far superior to the traditional front-engined cars. Cooper won seven races and two world championships before Cooper’s rivals caught up.

Brabham left Cooper at the end of the 1961 season to found his own team with his friend and engineer, Ron Tauaranc. His new car made its debut in 1962 but it needed a change in regulations in 1966, allowing a three-litre engine, for the Brabham to make its mark. The Australian Repco company built him a V8 engine and he scored his first victory at the wheel of his own car in the 1966 French Grand Prix.

He also won the British, Dutch and German races on the way to the title and his team-mate, Denny Hulme, won the drivers’ title the next year. He won his final grand prix in South Africa in 1970, when the future McLaren chief Ron Dennis was the team’s chief mechanic, before retiring.

"The word 'legend' is often used to describe successful sportsmen, but often it exaggerates their status. In the case of Sir Jack Brabham, however, it's entirely justified," said Dennis in a statement. "A three-time Formula 1 world champion, he remains the only driver to win a Formula 1 world championship driving a car bearing his own name – a unique achievement that will surely never be matched."

Brabham made his last public appearance on the Sunshine Coast on Sunday, where he was reunited with the 1967 BT23 race car he designed and built, the Sunshine Coast Daily said. Brabham’s three sons with his first wife, Betty, had careers in the sport and two grandsons are also involved in motor racing.